Oscillator system having a plurality of microelectromechanical resonators and method of designing, controlling or operating same

ABSTRACT

There are many inventions described and illustrated herein. In one aspect, the present inventions relate to oscillator systems which employ a plurality of microelectromechanical resonating structures, and methods to control and/or operate same. The oscillator systems are configured to provide and/or generate one or more output signals having a predetermined frequency over temperature, for example, (1) an output signal having a substantially stable frequency over a given/predetermined range of operating temperatures, (2) an output signal having a frequency that is dependent on the operating temperature from which the operating temperature may be determined (for example, an estimated operating temperature based on a empirical data and/or a mathematical relationship), and/or (3) an output signal that is relatively stable over a range of temperatures (for example, a predetermined operating temperature range) and is “shaped” to have a desired turn-over frequency.

BACKGROUND

There are many inventions described and illustrated herein. Theinventions relate to microelectromechanical and/or nanoelectromechanical(collectively hereinafter “microelectromechanical”) structures anddevices/systems including same; and more particularly, in one aspect, tooscillator systems employing microelectromechanical resonatingstructures, and methods to control and/or operate same.

Microelectromechanical systems, for example, gyroscopes, oscillators,resonators and accelerometers, utilize micromachining techniques (i.e.,lithographic and other precision fabrication techniques) to reducemechanical components to a scale that is generally comparable tomicroelectronics. Microelectromechanical systems typically include amicroelectromechanical structure fabricated from or on, for example, asilicon substrate using micromachining techniques. The operation and theresponse of the microelectromechanical structures depend, to asignificant extent, on the operating temperature of the structure.

Where the microelectromechanical system is, for example, a resonator,which is fabricated from or on silicon, the performance of themicroelectromechanical resonator is dependent on the operatingtemperature of the resonator. In this regard, temperature fluctuationsmay result in, for example, changes in (i) microelectromechanicalresonator geometry, (ii) microelectromechanical resonator mass, (iii)stresses or strains on the microelectromechanical resonator (forexample, changes in stresses/strains due to, among other things, thethermal coefficient of expansion of the resonator, substrate and/orpackaging (if any)), and (iv) the material properties of the resonator.Among thermally-induced changes, the elastic sensitivity of silicon totemperature often dominates in many silicon-based microelectromechanicalresonator designs, which often results in a resonator frequency shift inthe range of about −20 ppm/C to about −30 ppm/C.

As is well understood, the Young's modulus for most materials ofinterest changes with temperature according to known thermalcoefficients. For example, polysilicon has a first-order thermalcoefficient of −75 ppm/C. Furthermore, the geometry of a beam structurealso changes with temperature, generally expanding with increasing intemperature. Again, as an example, polysilicon has a thermal expansioncoefficient of 2.5 ppm/C.

For some beam designs and related modeling purposes, and given amaterial with an isotropic thermal coefficient of expansion, the effectof thermal expansion of the width of the beam is somewhat offset by theeffect of thermal expansion of the length of the beam. While it may bepossible to compensate for some thermally-induced changes in theresonator based on the coefficient of thermal expansion, the shift inYoung's modulus over temperature generally dominates in many resonatordesigns.

Setting aside electrostatic forces, the resonance frequency (f) of abeam may be characterized under these assumptions by the equation:$f = {\frac{1}{2\pi}\sqrt{\frac{k_{eff}}{m_{eff}}}}$where k_(eff) is the effective stiffness of the beam, and m_(eff) is theeffective mass of the beam which is often constant over temperature.

In most implementations, the resonance frequency of themicroelectromechanical resonator should remain substantially stable overa range of operating temperatures. This, however, will not normally bethe case as thermally induced changes to the Young's modulus (or othervariables) tend to change in the mechanical stiffness of the beam. Assuch, thermally-induced changes to the Young's modulus tend to causeconsiderable drift or change in the frequency of the output of theresonator. (See, for example, FIG. 1).

Given typical requirements for temperature stabilities ranging inmagnitude from 0.1 to 100 ppm, and common operating temperaturespecifications ranging from −40 C to +85 C, there is a need for atemperature stable frequency (over an operating temperature range) ofoutput signals of systems employing microelectromechanical resonators.

SUMMARY OF THE INVENTIONS

There are many inventions described and illustrated herein. The presentinventions are neither limited to any single aspect nor embodimentthereof, nor to any combinations and/or permutations of such aspectsand/or embodiments. Moreover, each of the aspects of the presentinventions, and/or embodiments thereof, may be employed alone or incombination with one or more of the other aspects of the presentinventions and/or embodiments thereof. For the sake of brevity, many ofthose permutations and combinations will not be discussed separatelyherein.

In one aspect, the present inventions are directed to a an oscillatorsystem, comprising (i) a first microelectromechanical resonator togenerate a first output signal having a frequency that varies withoperating temperature, wherein the first microelectromechanicalresonator includes a frequency function of temperature of the firstmicroelectromechanical resonator, and (ii) a secondmicroelectromechanical resonator to generate a second output signalhaving a frequency that varies with operating temperature, wherein thesecond microelectromechanical resonator includes a frequency function oftemperature of the second microelectromechanical resonator. Theoscillator system further includes frequency manipulation circuitry,coupled to the first and second microelectromechanical resonators togenerate a third signal having frequency that is substantially stableover a predetermined operating temperature using the first and secondoutput signals. The frequency manipulation circuitry may also becomprised of digital and/or analog circuitry, and/ormicroelectromechanical components to perform, for example, mixing and/orfiltering of the signals.

In one embodiment, the frequency manipulation circuitry is frequencysubtraction circuitry, for example, frequency mixer circuitry. Thefrequency subtraction circuitry may include filter circuitry, coupled tothe frequency mixer circuitry, to receive an output of the frequencymixer circuitry and to filter/attenuate a frequency sum component of theoutput of the frequency mixer circuitry. The frequency mixer circuitrymay include digital or analog circuitry.

The first and the second microelectromechanical resonators may bedisposed in or on the same substrate. Further, the firstmicroelectromechanical resonator and/or the secondmicroelectromechanical resonator may be fabricated from one or morematerials. In addition, the first and the second microelectromechanicalresonators may be fabricated from the same material. Indeed, the firstmicroelectromechanical resonator and the second microelectromechanicalresonator may be the same physical structure. Moreover, the firstmicroelectromechanical resonator, the second microelectromechanicalresonator and the frequency manipulation circuitry may be disposed in oron the same substrate, or disposed in or on different substrates.

In one embodiment, the first microelectromechanical resonator and thesecond microelectromechanical resonator include different crystallineorientations or directions in or on the same substrate. In anotherembodiment, the first microelectromechanical resonator and the secondmicroelectromechanical resonator are disposed in or on the differentsubstrates and/or fabricated from different materials.

In another aspect, the present inventions are directed to an oscillatorsystem, comprising (i) a first microelectromechanical resonator togenerate a first output signal having a frequency that varies withoperating temperature, wherein the first microelectromechanicalresonator includes a frequency function of temperature of the firstmicroelectromechanical resonator, and (ii) a secondmicroelectromechanical resonator to generate a second output signalhaving a frequency that varies with operating temperature, wherein thesecond microelectromechanical resonator includes a frequency function oftemperature of the second microelectromechanical resonator. Theoscillator system of this aspect includes frequency mixer circuitry,coupled to the first and second microelectromechanical resonators togenerate a third signal having a frequency that is substantially stableover an operating temperature using the first and second output signals.

In one embodiment of this aspect of the present inventions, thefrequency mixer circuitry further includes filter circuitry, coupled tothe frequency mixer circuitry, to receive an output of the frequencymixer circuitry and to filter/attenuate a frequency sum component of theoutput of the frequency mixer circuitry. The frequency mixer circuitrymay include, or be comprised of digital or analog circuitry.

In this aspect of the inventions, like the previous aspect of theinventions, the first microelectromechanical resonator and the secondmicroelectromechanical resonator may be disposed in or on the samesubstrate. Further, the first microelectromechanical resonator and thesecond microelectromechanical resonator may be fabricated from the samematerial. Indeed, the first microelectromechanical resonator and thesecond microelectromechanical resonator may be the same physicalstructure. Moreover, the first microelectromechanical resonator, thesecond microelectromechanical resonator and the frequency mixercircuitry may be disposed in or on the same substrate, or disposed in oron different substrates.

The first microelectromechanical resonator and the secondmicroelectromechanical resonator may include different crystallineorientations or directions in or on the same substrate. In anotherembodiment, the first microelectromechanical resonator and the secondmicroelectromechanical resonator are disposed in or on differentsubstrates and/or fabricated from different materials.

In yet another aspect, the present inventions are directed to anoscillator system, comprising (i) a first microelectromechanicalresonator to generate a first output signal having a frequency thatvaries with operating temperature, wherein the firstmicroelectromechanical resonator includes a frequency function oftemperature of the first microelectromechanical resonator, and (ii) asecond microelectromechanical resonator to generate a second outputsignal having a frequency that varies with operating temperature,wherein the second microelectromechanical resonator includes a frequencyfunction of temperature of the second microelectromechanical resonator.The oscillator system of this aspect of the inventions includesfrequency mixer circuitry, coupled to the first and secondmicroelectromechanical resonators to generate a third signal havingfrequency that is substantially stable over an operating temperatureusing the first and second output signals. In addition, the oscillatorsystem includes signal alignment circuitry, coupled to the frequencymixer circuitry, to generate an output signal having a frequency that isgreater than, less than, or equal to the frequency of the third signal.The signal alignment circuitry may also induce a phase change in theoutput signal with respect to the input signals.

In one embodiment of this aspect of the present inventions, thefrequency mixer circuitry further includes filter circuitry, coupled tothe frequency mixer circuitry, to receive an output of the frequencymixer circuitry and to filter/attenuate a frequency sum component of theoutput of the frequency mixer circuitry. As such, the signal alignmentcircuitry receives the output of the filter circuitry. Notably, thefrequency mixer circuitry may include, or be comprised of digital oranalog circuitry.

The signal alignment circuitry may include one or more phase lockedloops, delay locked loops, digital/frequency synthesizer and/orfrequency locked loops. In addition, the one or more digital/frequencysynthesizers may include one or more direct digital synthesizers,frequency synthesizers, fractional synthesizers and/or numericallycontrolled oscillators. Further, the one or more phase locked loops,delay locked loops, digital/frequency synthesizer and/or frequencylocked loops may include fractional and/or fine-fractional type phaselocked loops, delay locked loops, digital/frequency synthesizer and/orfrequency locked loops.

In this aspect of the inventions, like the previous aspects of theinventions, the first microelectromechanical resonator and the secondmicroelectromechanical resonator may be disposed in or on the samesubstrate. Further, the first microelectromechanical resonator and thesecond microelectromechanical resonator may be fabricated from the samematerial. Indeed, the first microelectromechanical resonator and thesecond microelectromechanical resonator may be the same physicalstructure. Moreover, the first microelectromechanical resonator, thesecond microelectromechanical resonator, the frequency mixer circuitryand signal alignment circuitry may be disposed in or on the samesubstrate, or disposed in or on different substrates.

Notably, the first microelectromechanical resonator and the secondmicroelectromechanical resonator may include different crystallineorientations or directions in or on the same substrate. In anotherembodiment, the first microelectromechanical resonator and the secondmicroelectromechanical resonator are disposed in or on differentsubstrates and/or fabricated from different materials.

Again, there are many inventions, and aspects of the inventions,described and illustrated herein. This Summary of the Inventions is notexhaustive of the scope of the present inventions. Moreover, thisSummary of the Inventions is not intended to be limiting of theinventions and should not be interpreted in that manner. While certainembodiments have been described and/or outlined in this Summary of theInventions, it should be understood that the present inventions are notlimited to such embodiments, description and/or outline, nor are theclaims limited in such a manner. Indeed, many others embodiments, whichmay be different from and/or similar to, the embodiments presented inthis Summary, will be apparent from the description, illustrations andclaims, which follow. In addition, although various features, attributesand advantages have been described in this Summary of the Inventionsand/or are apparent in light thereof, it should be understood that suchfeatures, attributes and advantages are not required whether in one,some or all of the embodiments of the present inventions and, indeed,need not be present in any of the embodiments of the present inventions.

BRIEF DESCRIPTION OF THE DRAWINGS

In the course of the detailed description to follow, reference will bemade to the attached drawings. These drawings show different aspects ofthe present inventions and, where appropriate, reference numeralsillustrating like structures, components, materials and/or elements indifferent figures are labeled similarly. It is understood that variouscombinations of the structures, components, materials and/or elements,other than those specifically shown, are contemplated and are within thescope of the present inventions.

FIG. 1 is a graphical illustration of the change of frequency of theoutput signal of a microelectromechanical resonator over a givenoperating temperature range of T₁ to T₂;

FIG. 2 is a graphical illustration of Young's modulus (E) versuscrystalline orientation of the microelectromechanical structure disposedin the (100) plane of monocrystalline silicon;

FIG. 3 is a block diagram representation of a microelectromechanicaloscillator system, including two microelectromechanical resonators andfrequency manipulation circuitry, according to certain aspects of thepresent inventions;

FIG. 4 is a graphical illustration of the change of frequency of theoutput signal of the two microelectromechanical resonators of FIG. 3over a given/predetermined operating temperature range of T₁ to T₂;

FIG. 5A is a block diagram representation of a microelectromechanicaloscillator system, including two microelectromechanical resonators andfrequency subtraction circuitry, according to certain aspects of thepresent inventions;

FIG. 5B is a block diagram representation of a microelectromechanicaloscillator system of FIG. 5A, wherein the frequency subtractioncircuitry includes frequency mixer circuitry, according to certainaspects of the present inventions;

FIGS. 6A and 6B are graphical illustrations of the change of frequencyof the output signals of the two microelectromechanical resonators andthe output of the frequency subtraction circuitry of FIG. 5A over agiven operating temperature range of T₁ to T₂, wherein the frequency ofthe output signal is relatively constant over the given/predeterminedoperating temperature range without exhibiting a “turn-over frequency”(see, FIG. 6A), and the frequency of the output signal, which isrelatively constant over the given/predetermined operating temperaturerange, including a “turn-over frequency” within the given/predeterminedoperating temperature range (see, FIG. 6B);

FIG. 7A is a block diagram representation of a microelectromechanicaloscillator system according to an embodiment of one aspect of thepresent inventions, wherein one or more of the microelectromechanicalresonators include a resonating beam (which is anchored at both ends);

FIG. 7B is a block diagram representation of a microelectromechanicaloscillator system according to another embodiment of one aspect of thepresent inventions, wherein one or more of the microelectromechanicalresonators are illustrated as “paddle” like resonating beams whichinclude layouts which are rotated relative to each other to providedifferent changes in Young's modulus over temperature due to thedifferent layout orientations;

FIG. 7C is a block diagram representation of a microelectromechanicaloscillator system according to another embodiment of one aspect of thepresent inventions, wherein the microelectromechanical resonators areillustrated as “paddle” like resonating beams which are coupled to acommon structure and include layouts which are rotated relative to eachother to provide different changes in Young's modulus over temperaturedue to the different layout orientations;

FIG. 7D is a block diagram representation of a microelectromechanicaloscillator system according to an embodiment of one aspect of thepresent inventions, wherein the microelectromechanical resonators arethe same resonating beam of the same physical structure which resonatein multiple, different eigen-modes of operation, for example, in-planeand out-of-plane or combinations of lateral or rotational modes thatexhibit different temperature coefficients;

FIGS. 8A-8D illustrate three-dimensional block diagram representationsof a plurality of exemplary embodiments of the microelectromechanicaloscillator having microelectromechanical resonators and/or frequencymanipulation circuitry integrated on/in a common and/or differentsubstrates, according to certain aspects of the present inventions;

FIGS. 8E-8K illustrate three-dimensional block diagram representationsof a plurality of exemplary embodiments of the microelectromechanicaloscillator having microelectromechanical resonators (i) integrated on/ina common and/or different substrates and (ii) fabricated from differentmaterials, according to certain aspects of the present inventions;

FIG. 9 is a block diagram representation of a microelectromechanicaloscillator system, wherein the frequency subtraction circuitry includesfrequency mixer circuitry and filter circuitry, according to certainaspects of the present inventions;

FIG. 10A is a block diagram representation of a microelectromechanicaloscillator system having two microelectromechanical resonators,frequency manipulation circuitry (here, frequency mixer circuitry) andcontrol circuitry to provide, generate and/or output a signal which isrepresentative of an operating temperature, according to certain aspectsof the present inventions;

FIG. 10B is a block diagram representation of a microelectromechanicaloscillator system having two microelectromechanical resonators,frequency manipulation circuitry (here, frequency mixer circuitry) andcontrol circuitry configured in a feedback architecture with drive andsense circuitry, according to certain aspects of the present inventions;

FIG. 10C is a block diagram representation of a microelectromechanicaloscillator system having two microelectromechanical resonators,frequency manipulation circuitry (here, frequency mixer circuitry) andcontrol circuitry to provide, generate and/or output a signal which isrepresentative of an operating temperature as well as to provide controlinformation to drive and sense circuitry, according to certain aspectsof the present inventions;

FIG. 10D is a block diagram representation of a microelectromechanicaloscillator system having two microelectromechanical resonators,frequency manipulation circuitry (here, frequency mixer circuitry),control circuitry and filter circuitry to provide, generate and/oroutput control information to drive and sense circuitry and provide,generate and/or output a signal which is relatively stable over at leasta given operating temperature range, according to certain aspects of thepresent inventions;

FIG. 10E is a block diagram representation of a microelectromechanicaloscillator system having two microelectromechanical resonators,frequency manipulation circuitry (here, frequency mixer circuitry) andcontrol circuitry and filter circuitry to provide, generate and/oroutput a signal which is relatively stable over at least a givenoperating temperature range as well as a signal which is representativeof the operating temperature of microelectromechanical resonators 12,according to certain aspects of the present inventions;

FIG. 10F is a block diagram representation of a microelectromechanicaloscillator system having two microelectromechanical resonators,frequency manipulation circuitry (here, frequency mixer circuitry) andcontrol circuitry configured to provide feedback to themicroelectromechanical resonators (for example, to adjust a bias voltageof one or more of the microelectromechanical resonators), according tocertain aspects of the present inventions;

FIGS. 11A and 11B are block diagram representations ofmicroelectromechanical oscillator systems having twomicroelectromechanical resonators and frequency addition circuitry (FIG.11A), wherein the frequency addition circuitry may be frequency mixercircuitry (FIG. 11B), according to certain aspects of the presentinventions;

FIGS. 12A and 12B are flow diagrams of exemplary processes to determineand/or identify a plurality of parameters to provide an output signalhaving a substantially stable frequency (i.e., constant, substantiallyconstant and/or essentially constant frequency) over a predeterminedrange of operating temperatures, according to certain exemplaryembodiments of the present inventions;

FIG. 13 is a graphical illustration of the change of frequency of theoutput signal of the two microelectromechanical resonators of FIG. 3wherein an offset is incorporated into configuring the oscillator systemto provide a “shaping” of the frequency response of the output of thefrequency manipulation circuitry to provide a turn-over region orfrequency around f_(m);

FIGS. 14A-14C are block diagram representations ofmicroelectromechanical oscillator systems, including three or moremicroelectromechanical resonators and frequency manipulation circuitry(for example, frequency subtraction circuitry and/or frequency additioncircuitry), according to certain aspects of the present inventions;

FIGS. 15A and 15B are block diagram representations of amicroelectromechanical oscillator system, including twomicroelectromechanical resonators and frequency manipulation circuitry,in conjunction with clock alignment circuitry, according to certainaspects of the present inventions;

FIGS. 16A and 16B illustrate three-dimensional block diagramrepresentations of a plurality of exemplary embodiments of themicroelectromechanical oscillator having (i) microelectromechanicalresonators and frequency manipulation circuitry and (ii) signal or clockalignment circuitry integrated on/in a common and/or differentsubstrates, according to certain aspects of the present inventions;

FIG. 16C illustrates a three-dimensional block diagram representation ofan exemplary embodiment of the microelectromechanical oscillator havingmicroelectromechanical resonators and frequency manipulation circuitryintegrated on/in a common and signal or clock alignment circuitryintegrated on/in a different substrate; and

FIGS. 17A-17M are block diagram illustrations of an oscillator systemaccording to aspects and/or embodiments of the present inventionswherein one or more electronic/electrical resonators each provide anoutput signal to the frequency manipulation circuitry, according tocertain aspects and/or embodiments of the present inventions.

DETAILED DESCRIPTION

There are many inventions described and illustrated herein. In oneaspect, the present inventions relate to oscillator systems which employa plurality of microelectromechanical resonators, and methods to controland/or operate same. The oscillator systems of the present inventionsmay be configured to provide and/or generate one or more output signalshaving a predetermined frequency over temperature, for example, (1) anoutput signal having a substantially stable frequency (i.e., constant,substantially constant and/or essentially constant frequency) over apredetermined range of operating temperatures, (2) an output signalhaving a frequency that is dependent on the operating temperature fromwhich the operating temperature may be determined (for example, anestimated operating temperature based on a empirical data and/or amathematical relationship), and/or (3) an output signal having asubstantially stable frequency over a range of temperatures (forexample, a predetermined operating temperature range) and is “shaped” tohave a desired turn-over frequency. Notably, “substantially stablefrequency” may be considered in view of, among other things, aparticular application over a particular, given or predetermined rangeof temperatures.

In one embodiment, the present inventions include an oscillator systemhaving two microelectromechanical resonators, each resonator having a“frequency function of temperature” (resulting from or caused by, forexample, a change in Young's modulus over temperature of themicroelectromechanical resonator (i.e., E(T) varies over temperature), achange in dimension of the microelectromechanical resonator overtemperature, a change in mass of the microelectromechanical resonatorover temperature, a change in stress/strain conditions of themicroelectromechanical resonator, the substrate and/or the housing). Inthis embodiment, the output of each microelectromechanical resonator,having a frequency that varies with temperature (for example, operatingtemperature), may be applied to frequency manipulation circuitry togenerate an output signal having a predetermined frequency that issubstantially stable (i.e., constant, substantially constant and/oressentially constant) over temperature (for example, over a given orpredetermined temperature range). The frequency manipulation circuitrymay, in addition to or in lieu thereof, generate an output signal havinga predetermined frequency that changes over temperature in apredetermined manner, or it may change in an indeterminate or hystereticmanner. For example, part or much of the change may be in apredetermined manner while another part or portion of the change may beindeterminate or hysteretic.

Notably, the frequency manipulation circuitry may be implemented asdigital and/or analog circuitry. In addition thereto, or in lieuthereof, the frequency manipulation circuitry may be implemented asmicroelectromechanical components. There are many types, designs and/orconfigurations of frequency manipulation circuitry. All such circuitry,whether now known of later developed, are intended to fall within thescope of the present inventions.

In one embodiment, the output signal having the substantially stablefrequency (i.e., constant, substantially constant and/or essentiallyconstant frequency) over, for example, a predetermined temperaturerange, may be employed as an output signal and/or may be applied tosignal or clock (hereinafter collectively “clock”) alignment circuitry(for example, one or more phase locked loops (PLLs), delay locked loops(DLLs), digital/frequency synthesizer, for example, a direct digitalsynthesizer (“DDS”), frequency synthesizer, fractional synthesizerand/or numerically controlled oscillator, and/or frequency locked loops(FLLs)) to adjust (for example, increase or decrease) and/or control thefrequency of the output signal of the microelectromechanicalresonator-based oscillator system. In this way, the clock signal mayinclude a predetermined frequency that is higher or lower in frequencythan the frequency of the output signal of the oscillator system.Indeed, the clock alignment circuitry may provide a plurality of outputsignals that are higher and/or lower in frequency than the frequency ofthe output signal of the oscillator system.

Where an output signal of the frequency manipulation circuitry changesover temperature in a predetermined manner, that signal may be employedas a measure of the operating temperature of the system. In oneembodiment, the signal which is representative of the operatingtemperature of the oscillator system may be applied to controlcircuitry, in a feedback loop, which adjusts the drive and/or sensecircuitry of one or more of the resonators or other (different)microelectromechanical-type elements or structures, for example,microelectromechanical gyroscopes or accelerometers that are, forexample, disposed on or in the same substrate. In this way, the outputsignal of the oscillator system may include a substantially stablefrequency via control or adjustment of the drive and/or sense circuitryof one or more of the microelectromechanical resonators.

Notably, the frequency manipulation circuitry may provide a plurality ofoutputs including one or more output signals (i) having a frequency (forexample, a predetermined frequency) that is substantially stable (i.e.,constant, substantially constant and/or essentially constant) overtemperature (for example, over a given or predetermined temperaturerange), and/or (ii) having a frequency that changes over temperature(for example, over a given or predetermined temperature range) in apredetermined manner. All permutations and combinations of outputs ofthe frequency manipulation circuitry are intended to fall within thescope of the present inventions.

The microelectromechanical resonators may be disposed (1) on/in the samesubstrate and fabricated from the same material, (2) on/in differentsubstrates from the same material, (3), on/in the same substrate butfrom different materials, and/or (4) on/in different substrates ofdifferent materials. For example, where the resonators are disposed onthe same substrate and in the same material (for example,monocrystalline silicon) or in/on different substrates of the samematerial, the resonators may be fabricated in/on the substrate indifferent orientations or directions. In this way, although theresonators are fabricated from or in the same material having the sameor substantially the same mechanical properties, the Young's modulus ofeach resonator structure may be different and may vary or changedifferently over temperature (i.e., dE/dT of one resonator structure isdifferent from the dE/dT of the other resonator structure, or E(T) ofone resonator structure is different from E(T) of the other resonatorstructure, where E(T) is the function of Young's modulus overtemperature) due to the different crystalline orientations (for example,where the material is silicon, the strain field of one of the resonatorsmay be predominantly oriented in the <100> direction in the (100) plane,and the strain field of the other resonator may be disposed in the <110>direction on the (100) plane (stated differently, the two strain fieldsare oriented at an angle of 45° with respect to each other in the (100)plane)). (See, for example, FIG. 2). Resonator designs that incorporatestrain energy in multiple directions and/or multiple materials are alsopossible and indeed may be advantageous. For example a pair of resonatorstructures may have strain fields that are not oriented purely in <100>and <110> directions, thereby forming resonators with intermediate“aggregate” material properties.

Notably, where the microelectromechanical resonators are disposed on/inthe same substrate and fabricated from different materials, and/or on/indifferent substrates from different materials, the Young's modulus ofeach resonator structure may be different and may also vary or changedifferently over temperature (i.e., dE/dT of one resonator structure isdifferent from the dE/dT of the other resonator structure, or E(T) ofone resonator is different from E(T) of the other resonator) due to thedifferences in the properties, for example, mechanical properties, ofthe different materials. As such, the crystalline orientations (if any)of the microelectromechanical resonators may or may not be different.

Further, at least one resonator may be created from a compositematerial, for example, a combination of silicon, silicon nitride, and/orsilicon dioxide. The relative amounts of materials and their location inthe resonator device may be adjusted to advantageously influence thefrequency function of temperature of each.

With reference to FIG. 3, in one aspect, the present inventions aredirected to microelectromechanical oscillator system 10 havingmicroelectromechanical resonators 12 a and 12 b and frequencymanipulation circuitry 14. The output signal of microelectromechanicalresonator structure 12 a includes a resonant frequency f₁ that variesover temperature. The output signal of resonator structure 12 b includesa resonant frequency f₂ that varies over temperature. Moreover, withreference to FIG. 4, microelectromechanical resonator structure 12 aincludes a Young's modulus which changes over operating temperature(i.e., non-zero dE/dT or varying E(T)) in a manner and/or rate that isdifferent from the manner and/or rate of the Young's modulus change overtemperature of microelectromechanical resonator structure 12 b.

In one embodiment, the resonant frequency f₁ and resonant frequency f₂are different frequencies. In this embodiment, frequency manipulationcircuitry 14 may generate an output signal having a frequency (f_(m))that is substantially stable over temperature. In one embodiment,frequency manipulation circuitry 14 may generate an output signal havingsubstantially stable frequency (f_(m)) by “subtracting” the frequenciesof the output signals of microelectromechanical resonator structure 12 aand microelectromechanical resonator structure 12 b. With reference toFIGS. 5A and 6, in this embodiment, frequency manipulation circuitry 14is comprised of frequency subtraction circuitry 14 a.

The resonant frequency of a mass-spring system may be characterized as$f = {\frac{1}{2\pi}\sqrt{\frac{k}{m}}}$

where f is the resonant frequency of the system, k is the mechanicalspring constant, and m is the movable mass. In many systems, the springconstant may be a function of the material stiffness, materialdimensions, material composition, direction of bending, presence ofstresses or strains, and surrounding fluids or gasses, some or all ofwhich may be a function of temperature. In addition, the mass may changewith temperature due to, for instance, evaporation and condensation. Insome cases, the effect of Young's modulus will be the dominant factor.The frequency function of temperature may be expressed as:${f(T)} = {\frac{1}{2\pi}\sqrt{\frac{k_{0}}{m_{0}}\left( {1 + {\alpha\left( {T - T_{0}} \right)} + {\beta\left( {T - T_{0}} \right)}^{2} + {\gamma\left( {T - T_{0}} \right)}^{3} + \ldots}\quad \right)}}$where k₀ and m₀ are the stiffness and mass, respectively, at referencetemperature T₀. Substituting a reference frequency$f_{o} = {\frac{1}{2\pi}\sqrt{\frac{k_{0}}{m_{0}}}}$into the equation above, and truncating at the third-ordertemperature-dependent term for compactness and/or simplification, thefrequency function of temperature may be expressed as:f(T)=f ₀√{square root over ((1+α(T−T ₀)+β(T−T ₀)²+γ(T−T ₀)³))}Using the Taylor expansion about reference temperature T₀, thisexpression may be simplified as:f(T)=f ₀(1+α(T−T ₀)+b(T−T ₀)² +c(T−T ₀)³)where${a = \frac{\alpha}{2}},{b = \frac{\beta}{2}},{{{and}\quad c} = {\frac{\gamma}{2}.}}$Generally, the frequency function of temperature for resonator “n” maybe expressed as:f _(n)(T)=f _(nT(0))(1+α_(n)(T−T ₀)+b _(n)(T−T ₀)² +c _(n)(T−T ₀)³).The adverse impact on the frequency of the output of the resonator dueto temperature variations may be offset, reduced and/or minimized bycancelling and/or addressing the impact of at least one of thetemperature-dependent terms in the equation above. As such, thefrequency outputs of two resonators may be combined as follows:f _(m)(T)=±f ₁(T)±f ₂(T).

Notably, the sign of f₁(T) and f₂(T) in the equation immediately abovemay be “selected” to provide for one or more predeterminedtemperature-dependence terms to cancel and/or offset the temperatureimpact on the output frequency. In this regard, when the temperaturedependence of the frequency for each resonator are of similar sign, forexample, and the slopes of the temperature dependence of frequency ofthe resonators have the same orientation, frequency manipulationcircuitry 14 may generate an output signal having a frequency (f_(m))that is substantially stable over a predetermined/given temperaturerange by “subtracting” the frequencies of microelectromechanicalresonators 12 a and 12 b. When the temperature dependence of thefrequency for each resonator is opposite, for example, the slopes of thetemperature dependence of frequency of the resonators are opposite, andfrequency manipulation circuitry 14 may generate an output signal havinga frequency (f_(m)) that is substantially stable over apredetermined/given temperature range by “adding” the frequencies ofmicroelectromechanical resonators 12 a and 12 b.

For example, where the characteristics of microelectromechanicalresonators 12 a and 12 b include a similar change over temperature (forexample, microelectromechanical resonators 12 a and 12 b include thesame slope of temperature dependence of the frequency), frequencymanipulation circuitry 14 may “subtract” the output signal of secondmicroelectromechanical resonator 12 b from the output signal of firstmicroelectromechanical resonator 12 a, and setting the first ordertemperature dependence term to zero provides two equationsf _(1T(0)) −f _(2T(0)) =f _(mT(0))a ₁ f _(1T(0)) −a ₂ f _(2T(0))=0where f_(mT(0)) is the output frequency at the reference temperature.This may provide the relationship of${\frac{f_{1{T{(0)}}}}{f_{2{T{(0)}}}} = \frac{a_{2}}{a_{1}}},$and per the sign convention of positive frequencies, f_(1T(0))>f_(2T(0))and$f_{1{T{(0)}}} = {{\frac{f_{{mT}{(0)}}}{1 - \frac{a_{1}}{a_{2}}}\quad{and}\quad f_{2{T{(0)}}}} = {\frac{a_{1}}{a_{2}}f_{1{T{(0)}}}}}$where: ${\frac{a_{2}}{a_{1}} > 0},$and a₁<a₂

In one exemplary embodiment, in the context of monocrystalline silicon,the strain field of microelectromechanical resonator 12 a may bepredominantly oriented in the <110> direction in the (100) plane, andthe strain field of microelectromechanical resonator 12 b may bedisposed in the <100> direction on the (100) plane (stated differently,the two strain fields are oriented at an angle of 45° with respect toeach other in the (100) plane)). (See, for example, FIGS. 7B and 7C). Assuch, Young's modulus of microelectromechanical resonators 12 a and 12 bare different, and the manner and/or rate of change of Young's modulusof microelectromechanical resonators 12 a and 12 b differ over operatingtemperature (i.e., E(T) differs). Some example parameters may be foundin literature or derived/obtained from data reported in literature.Notably, certain of these parameters have recently been measured asa₁=−19.0×10⁻⁶/C, a₂=−28.5×10⁻⁶/C, leading to a1/a2=2/3. Different ratiosof a₁/a₂ may be obtained as the stress fields in one or more resonatordevices may be distributed across multiple orientations in the samematerial or through multiple materials in a composite structure.

Using such typical values and the relationships off_(mT(0))=f_(1T(0))−f_(2T(0)),${\frac{f_{1{T{(0)}}}}{f_{2{T{(0)}}}} = \frac{a_{2}}{a_{1}}},$and${f_{{mT}{(0)}} = {f_{1{T{(0)}}}\left( {1 - \frac{a_{1}}{a_{2}}} \right)}},$then f_(1T(0))≅3f_(mT(0)) and f_(2T(0))≅2f_(mT(0)) since$\frac{a_{1}}{a_{2}} \cong {\frac{2}{3}.}$The frequency manipulation circuitry 14 (which, in this example,includes frequency subtraction circuitry 14 a) may provide and/orgenerate an output signal having a frequency (f_(m)) of, for example,approximately 100 kHz, which is substantially stable over a given orpredetermined operating temperature range, employingmicroelectromechanical resonator structure 12 a having a frequency(f_(1T(0))) of approximately 300 kHz and a microelectromechanicalresonator structure 12 b having a frequency (f_(2T(0))) of approximately200 kHz. Thus, in this exemplary embodiment, although (i) the outputsignal of microelectromechanical resonator structure 12 a includes aresonant frequency f₁ which varies over operating temperature, and (ii)the output signal of resonator structure 12 b includes a resonantfrequency f₂ which also varies over operating temperature, frequencymanipulation circuitry 14 (which includes, in this example, frequencysubtraction circuitry 14 a) may generate and/or provide an output signalhaving a frequency (f_(m)) that is substantially stable over, forexample, a given or predetermined temperature range. (See, for example,FIGS. 6A and/or 6B).

Notably, with reference to FIG. 6B, and the output signal, which isrelatively constant over the given/predetermined operating temperaturerange, may include a “turn-over frequency” within thegiven/predetermined operating temperature range (see, FIG. 6B). The“turn-over” frequency may be provided since the frequency responses ofmicroelectromechanical resonator structure 12 a and 12 b may not beperfectly linear and, as such, the “turn-over” frequency may occur bysimply eliminating the first order coefficient from thetemperature-dependent frequency function.

With reference to FIG. 5B, in one embodiment, frequency subtractioncircuitry 14 a includes frequency mixer circuitry 16 to generate anoutput signal having substantially stable frequency (f_(m)) overtemperature (for example, a given or predetermined temperature range).The frequency mixer circuitry 16 is well known circuitry which provides,generates and/or produces a signal that includes a frequency of the“difference” between the frequencies of the two input signals (the“frequency difference component”) and a signal that includes a frequencyof the “sum” of the frequencies of the two input signals (the “frequencysum component”). The “frequency difference” component of the outputsignal of frequency mixer circuitry 16 may be employed as an outputsignal having a frequency (f_(m)) that is substantially stable over, forexample, a given or predetermined temperature range. Notably, thefrequency mixer circuitry may be current based or voltage based. Indeed,all forms, types and architectures of frequency mixer circuitry, whethernow known or later developed, are intended to fall within the scope ofthe present inventions.

For example, frequency subtraction circuitry 14 a and/or frequency mixercircuitry 16 may be implemented as digital and/or analog circuitry. Assuch, the subtraction operation may be performed in the digital domainand/or analog domain. For example the frequency subtraction circuitrymay be frequency mixer or multiplier circuitry or more generally anynon-linear circuitry with two or more inputs and at least one output.Again, the circuit may be digital and/or analog circuitry, such as anXOR gate or more complex circuitry, for example frequency comparisoncounters with electronic oscillator and control loop. Such circuitry mayinclude one or more microelectromechanical elements that might beseparate from the resonators or might be part of the resonators. Again,all forms, types and architectures of frequency subtraction circuitry 14a and/or frequency mixer circuitry 16, whether now known or laterdeveloped, are intended to fall within the scope of the presentinventions.

The microelectromechanical resonators 12 may employ any type ofmicroelectromechanical resonator design, architecture and/or control,whether now known or later developed; and all suchmicroelectromechanical resonator designs, architectures and/or controltechniques are intended to fall within the scope of the presentinventions. (See, for example, FIGS. 7A-7C). For example,microelectromechanical resonators 12 may include a resonating beam whichis anchored at both ends. (See, for example, FIG. 7A). Moreover,microelectromechanical resonators 12 may include a paddle-like design.(See, for example, FIG. 7B). Indeed, microelectromechanical resonators12 may be components or portions of the same physical structure (see,for example, FIG. 7C) and/or microelectromechanical resonators 12 may bethe same component or portion of the same physical structure thatresonate in multiple, different modes of operation, for example,in-plane and out-of-plane (see, for example, FIG. 7D). Again, allmicroelectromechanical resonator designs, structures, architecturesand/or control techniques, whether now known or later developed, areintended to fall within the scope of the present inventions.

Further, microelectromechanical resonators 12 may be fabricated and/orpackaged using any fabrication and/or packaging techniques whether nowknown or later developed. Indeed, all such fabrication and/or packagingtechniques are intended to fall within the scope of the presentinventions.

The microelectromechanical resonators 12 may be disposed on/in the samesubstrate or on/in different substrates. Moreover, frequencymanipulation circuitry 14 may be disposed on/in the same substrates asone or more microelectromechanical resonators 12, or on/in a differentsubstrate. In particular, microelectromechanical resonators 12 and/orfrequency manipulation circuitry 14 may be integrated on/in the samesubstrate 18 (see, for example, FIG. 8A), on/in different substrates 18a, 18 b and 18 c (see, for example, FIG. 8B), on/in different substrates18 a and 18 b (see, for example, FIGS. 8C and 8D). All permutations andcombinations thereof are intended to fall within the scope of thepresent inventions.

Moreover, microelectromechanical resonators 12 may be fabricated, inwhole or in part, in/from the same materials or different materials.(See, for example, FIGS. 8E-8K). For example, microelectromechanicalresonators 12 may be integrated on/in the same substrate 18 and in/fromdifferent materials (see, for example, FIGS. 8E, 8F and 8I) such as asubstrate having monocrystalline silicon and polycrystalline siliconwherein microelectromechanical resonator structure 12 a is fabricatedin/on monocrystalline silicon and microelectromechanical resonatorstructure 12 b is fabricated in/on polycrystalline silicon. Further,microelectromechanical resonators 12 may be integrated on/in differentsubstrates 18 a and 18 b and in/from different materials (see, forexample, FIGS. 8G and 8H). Moreover, frequency manipulation circuitry 14and one or more microelectromechanical resonators 12 may also befabricated in/from the same or different materials (see, for example,FIGS. 8J and 8K). All permutations and combinations thereof are intendedto fall within the scope of the present inventions. Moreover, asmentioned above, any fabrication and packaging technique and/or processmay be implemented.

Notably, in those instances where microelectromechanical resonators 12and/or frequency manipulation circuitry 14 (and/or clock alignmentcircuitry) are fabricated in/on separate substrates, the various signalsmay be provided using electrical interconnects (not illustrated)connecting bond pads (not illustrated) located in/on substrates and/orflip-chip techniques. Where microelectromechanical resonators 12 and/orfrequency manipulation circuitry 14 are fabricated in/on the samesubstrate, the various signals may be provided using interconnectionsdisposed in/on the substrates. The present inventions may employ anyinterconnect or interconnection technique/architecture whether now known(for example, wire bonding) or later developed. All suchtechniques/architectures are intended to fall within the scope of thepresent inventions.

The output signal of microelectromechanical oscillator system 10 may besingle ended or double ended (i.e., differential signaling). The “shape”of the output signal (for example, square, pulse, sinusoidal or clippedsinusoidal) may be predetermined and/or programmable. In this regard,information which is representative of the “shape” of the output signalmay be stored or programmed in memory (which is resident in frequencymanipulation circuitry 14 and/or the clock alignment circuitry (if any)during fabrication, test, calibration and/or operation. In this way,frequency manipulation circuitry 14 and/or the clock alignment circuitry(if any) may access a resident memory to obtain such information duringstart-up/power-up, initialization, re-initialization and/or duringnormal operation of frequency manipulation circuitry 14 and/or the clockalignment circuitry.

With reference to FIG. 9, in one embodiment, frequency manipulationcircuitry 14 includes frequency mixer circuitry 16 and filter circuitry20. In this embodiment, frequency mixer circuitry 16 provides, generatesand/or produces a signal having a frequency that is representative ofthe “difference” between the frequencies of the two input signals and asignal having a frequency that is representative of the “sum” of thefrequencies of the two input signals. The filter circuitry 20 mayattenuate/filter the output of frequency mixer circuitry 16 to provideeither the “frequency difference component” or the “frequency sumcomponent” of the output signal of frequency mixer circuitry 16. Forexample, where an output signal having a substantially stable frequencyover temperature is desired (and, for example, the change in Young'smodulus over temperature of microelectromechanical resonators 12 a and12 b is the same or substantially the same), a lowpass or bandpassfilter may be employed to attenuate the frequency sum component of theoutput signal of frequency mixer circuitry 16. In this way, anyinterference by the frequency sum component to further processing of thefrequency difference component of the output signal (which includes asubstantially stable frequency over temperature) of frequency mixercircuitry 16 may be minimized and/or reduced.

In contrast, where an output signal having a frequency response thatchanges over operating temperature is desired, a highpass or bandpassfilter may be employed to attenuate the frequency difference componentof the output signal of frequency mixer circuitry 16. Thus, in thisembodiment, interference by the frequency difference component of theoutput signal to additional processing of the frequency sum component isminimized and/or reduced.

Notably, all forms, types and architectures of (i) filter circuitry,including digital or analog circuitry, and (ii) processing, includingdigital or analog, whether now known or later developed, are intended tofall within the scope of the present inventions.

In one embodiment, frequency manipulation circuitry 14 may, in additionto or in lieu thereof, generate an output signal having a predeterminedfrequency that changes over temperature in a predetermined manner. Forexample, where frequency manipulation circuitry 14 is frequency mixercircuitry 16, the frequency sum component may be employed as a signalwhich is representative of the operating temperature ofmicroelectromechanical resonator structure 12 a and/ormicroelectromechanical resonator structure 12 b. In this regard, thefrequency of the signal which is the frequency sum component isdependent on the operating temperature of microelectromechanicalresonator structure 12 a and/or microelectromechanical resonatorstructure 12 b and, as such, control circuitry may be employed tointerpret, analyze and/or correlate the frequency of the signal which isthe frequency sum component to an operating temperature.

With reference to FIG. 10A, in one embodiment, oscillator system 10employs control circuitry 22 to interpret, analyze and/or correlate thefrequency of the signal which is the frequency sum component to anoperating temperature. The control circuitry 22, in one embodiment,employs a look-up table (based on empirical and/or theoretical data)and/or a predetermined or mathematical relationship to interpret,analyze and/or correlate the frequency of the frequency sum component toan operating temperature. The control circuitry 22 may generate and/orprovide temperature sensor data which is representative of the operatingtemperature to other circuitry.

Moreover, with continued reference to FIG. 10A, resonator drive andsense circuitry 24 drives an associated microelectromechanical resonator12 and senses an output signal therefrom. The resonator drive and sensecircuitry 24, as well as drive and sense electrodes (not illustrated),may be conventional well-known drive and sense circuitry. Indeed, driveand sense circuitry 24 may be any microelectromechanical drive and sensecircuitry whether now known or later developed. For example, drive andsense circuitry 24 may be configured to provide a single-ended outputsignal or differential output signals.

Notably, drive and sense circuitry 24 may be integrated on the samesubstrate in which the associated microelectromechanical resonator 12resides (or is fabricated in). In addition, or in lieu thereof, driveand sense circuitry 24 may be integrated on a substrate that isphysically separate from (and electrically connected with) the substratein which the associated microelectromechanical resonator 12 resides.

In addition, drive and sense electrodes (not illustrated), may be of aconventional, well known type or may be any type and/or shaped electrodewhether now known or later developed. Further, the physical electrodesand/or other portions of microelectromechanical resonator 12 mayinclude, for example, capacitive, piezoresistive, piezoelectric,inductive, magnetorestrictive and/or thermal transduction mechanisms.Indeed, all physical transduction mechanisms whether now known or laterdeveloped for microelectromechanical systems are intended to fall withinthe scope of the present inventions.

In one embodiment, control circuitry 22, in response to such temperaturedata, may adjust and/or control the operation of one or more ofmicroelectromechanical resonators 12 (via the associated resonator driveand sense circuitry 24) to compensate, address and/or correct for, forexample, variations of the material properties and/or manufacturingvariances of the fabrication processes (and/or for changes in operatingtemperature of microelectromechanical resonators 12). (See, for example,FIG. 10B). In this regard, the actual frequency of the output of one ormore microelectromechanical resonators 12 may require modificationand/or adjustment and/or the materials may include differing mechanicalproperties from anticipated/designed. Accordingly, in one embodiment,control circuitry 22 may instruct and/or cause resonator drive and sensecircuitry 24 to adjust, for example, the bias drive for one or more ofmicroelectromechanical resonators 12. In this way, the characteristicsof the output signal (for example, frequency) of one or more ofmicroelectromechanical resonators 12 may be adjusted and/or controlledafter fabrication and/or in situ. Notably, this process may be repeateduntil a predetermined (whether before or after fabrication) and/or moredesirable or optimum performance of oscillator system 10 is obtained.

With reference to FIG. 10C, in another embodiment, control circuitry 22,in addition to adjusting and/or controlling the operation of one or moreof microelectromechanical resonators 12 (via the associated resonatordrive and sense circuitry 24) using temperature data from frequencymanipulation circuitry, may also provide an output signal which isrepresentative of the operating temperature of microelectromechanicalresonators 12. In this way, other circuitry may employ the temperaturerelated data to control, adjust and/or change such circuitry inaccordance with operating temperature.

In addition, with reference to FIG. 10D, in another embodiment,oscillator 10 includes filter circuitry 20 a and filter circuitry 20 bto selectively attenuate one of the signals generated by frequencymanipulation circuitry 14. For example, where frequency mixer circuitry16 generates a difference signal which includes a frequency that isrelatively stable over a predetermined operating temperature, filtercircuitry 20 a may attenuate the “frequency sum component” of the outputsignal of frequency mixer circuitry 16 and output the “frequencydifference component”. In contrast, filter circuitry 20 b may attenuatethe “frequency difference component” of the output signal of frequencymixer circuitry 16 and provide the “frequency sum component” of theoutput signal to control circuitry 22 to adjust and/or control theoperation of one or more of microelectromechanical resonators 12 (viathe associated resonator drive and sense circuitry 24) using temperaturedata from frequency manipulation circuitry, may also provide an outputsignal which is representative of the operating temperature ofmicroelectromechanical resonators 12. In this way, for example, othercircuitry may employ the temperature related data to control, adjustand/or change such circuitry in accordance with operating temperature.

With reference to FIG. 10E, in another embodiment, oscillator 10includes filter circuitry 20 a and filter circuitry 20 b to selectivelyattenuate one of the signals generated by frequency manipulationcircuitry 14 (here illustrated as frequency mixer circuitry 16). In thisregard, frequency mixer circuitry 16 generates a “frequency sumcomponent” and a “frequency difference component”. The filter circuitry20 a may attenuate one of the components (for example, the “frequencysum component” of the output signal of frequency mixer circuitry 16) andoutput the “frequency difference component” as a signal having arelatively stable frequency over temperature. The filter circuitry 20 bmay attenuate the other component (in this example, the “frequencydifference component” of the output signal of frequency mixer circuitry16) and provide the “frequency sum component” of the output signal tocontrol circuitry 22 to provide an output signal which is representativeof the operating temperature of microelectromechanical resonators 12. Inthis way, for example, other circuitry may employ the temperaturerelated data to control, adjust and/or change such circuitry inaccordance with operating temperature.

Although the discussion above indicates that control circuitry 22 mayprovide feedback related information to one or more of resonator driveand sense circuitry 24 in order to adjust and/or control the operationof one or more of microelectromechanical resonators 12 (via theassociated resonator drive and sense circuitry 24), the feedback relatedinformation may be applied directly to one or more ofmicroelectromechanical resonators 12 to compensate, address and/orcorrect, for example, variations of the material properties and/ormanufacturing variances of the fabrication processes and/or for changesin operating temperature of microelectromechanical resonators 12). (See,for example, FIG. 10F).

Notably, all permutations and combinations of employing the output offrequency manipulation circuitry 14 (for example, the “frequency sumcomponent” and the “frequency difference component” of frequency mixercircuitry 16) in conjunction with, for example, control circuitry 20 andresonator drive and sense circuitry 24, are intended to fall within thescope of the present inventions. For the sake of brevity, suchpermutations and combinations with not be discussed in detail.

As mentioned above, all types and techniques of control and sense,whether now known or later developed, may be employed with respect toone or more of microelectromechanical resonators 12. All such techniquesand circuitry are intended to fall within the scope of the presentinventions.

As mentioned above, frequency manipulation circuitry 14 may includecircuitry to perform and/or implement subtraction (wherein circuitry 14includes frequency subtraction circuitry 14 a to generate an outputsignal which is representative of the difference of the frequencies ofresonator structures 12) and/or addition (wherein circuitry 14 includesfrequency addition circuitry 14 b, for example, frequency mixercircuitry 16 (as discussed above), to generate an output signal which isrepresentative of the sum of the frequencies of resonator structures12). (See, for example, FIGS. 5A, 5B, 11A and 11B). In theseembodiments, depending upon the temperature dependence of thefrequencies of each microelectromechanical resonator 12 and the desiredqualities of the output signal, frequency manipulation circuitry 14 maygenerate an output signal having a frequency (f_(m)) that is relativelystable over a given or predetermined temperature range and/or thatchanges over a given or predetermined temperature range in apredetermined manner. As such, frequency manipulation circuitry 14 mayprovide a signal or signals having a frequency or frequencies thatis/are relatively stable over a given or predetermined temperature rangeand/or representative of the operating temperature ofmicroelectromechanical resonator structure 12 a and/ormicroelectromechanical resonator structure 12 b.

Notably, frequency manipulation circuitry 14 may be implemented asdigital and/or analog circuitry. As such, the addition and subtractionoperations may be performed in the digital domain and/or analog domain.Again, all forms, types and architectures of frequency subtractioncircuitry 14 a and frequency addition circuitry 14 b, whether now knownor later developed, are intended to fall within the scope of the presentinventions.

Although not illustrated in detail, oscillator system 10 implementingfrequency addition circuitry 14 b may include control circuitry 22 tointerpret, analyze and/or correlate the frequency of the output signalof frequency manipulation circuitry 14 to an operating temperature ofone or more of resonator structures 12. The control circuitry 22, in oneembodiment, may employ a look-up table (based on empirical and/ortheoretical data) and/or a predetermined or mathematical relationship tointerpret, analyze and/or correlate the frequency of the output signalto an operating temperature. The control circuitry 22 may generateand/or provide temperature sensor data which is representative of theoperating temperature to other circuitry and/or drive and sensecircuitry 24 (as mentioned above).

Notably, in one embodiment, the resonant frequency (f₁) of resonatorstructure 12 a and the resonant frequency (f₂) of resonator structure 12b are the same frequency. In this embodiment, frequency manipulationcircuitry 14 may generate an output signal having a frequency (f_(m))that changes over temperature in a predetermined manner. As mentionedabove, under these circumstances, the frequency manipulation circuitry14 may generate and/or output a signal which is representative of theoperating temperature of microelectromechanical resonator structure 12 aand/or microelectromechanical resonator structure 12 b.

In one embodiment, oscillator system 10 employs control circuitry 22 tointerpret, analyze and/or correlate the frequency of the output signalto an operating temperature. The control circuitry 22, as mentionedabove, employs a look-up table (based on empirical and/or theoreticaldata) and/or a predetermined or mathematical relationship to interpret,analyze and/or correlate the frequency of the frequency sum component toan operating temperature. The control circuitry 22 may generate and/orprovide temperature sensor data which is representative of the operatingtemperature to other circuitry.

In another embodiment, control circuitry 22 may adjust, correct and/orcontrol one or more of microelectromechanical resonators 12 to, forexample, provide a signal having a frequency within a given,predetermined and/or desired range. For example, control circuitry 22may adjust, correct and/or control the frequency of the output ofresonator structure 12 a and/or the frequency of the output of resonatorstructure 12 b. In this regard, based on the frequency of thetemperature dependent signals, control circuitry 22, in one embodiment,may employ a look-up table (based on empirical and/or theoretical data)and/or a predetermined or mathematical relationship to adjust and/orcontrol the operation of one or more of resonator structure 12 a and/orthe frequency of the output of resonator structure 12 b. In this way, amore enhanced, desired and/or optimum performance of oscillator system10, and/or a predetermined frequency of the output signal of frequencymanipulation circuitry 14 may be obtained and/or provided given theoperating performance, conditions and/or environment of resonators 12and/or frequency manipulation circuitry 14.

In another aspect, the present inventions are directed to a method ofdesigning, determining and/or selecting parameters and/or features ofone or more aspects of oscillator system 10. With reference to FIG. 12A,in one embodiment, the method includes identifying a desired frequency(f_(m)) of the temperature-stable output signal. (See, 26 a). Forexample, a substantially stable frequency (f_(m)) over temperature ofapproximately 100 kHz.

Thereafter, the exemplary method may select and/or identify thematerials, the material properties and/or resonator characteristics ofeach microelectromechanical resonator, (for example, a₁, a₂, E₁, E₂).(See, 26 b). For example, as mentioned above, as reported in literatureor derived/obtained from data reported in literature, formonocrystalline silicon (1) E₁=168.9 GPa, and (2) E₂=130.2 GPa. Notably,other parameters have recently been measured as a₁=−19.0×10⁻⁶/C,a₂=−28.5×10⁻⁶/C.

After selecting and/or identifying the materials and material propertiesand/or resonator characteristics, design microelectromechanicalresonator structure 12 a to provide a frequency (f_(1T(0))) using, forexample,$f_{1{T{(0)}}} = {\frac{f_{{mT}{(0)}}}{1 - \frac{a_{1}}{a_{2}}}.}$In this exemplary embodiment, microelectromechanical resonator structure12 a provides an output signal having a frequency (f_(1T(0))) ofapproximately 300 kHz. (See, 26 c).

With continued reference to FIG. 12A, microelectromechanical resonatorstructure 12 b may be designed/defined using, for example, f₂=f₁−f_(m),microelectromechanical resonator structure 12 b provides an outputsignal having a frequency (f_(2T(0))) of approximately 200 kHz. (See, 26d).

Thus, using the exemplary process flow of FIG. 12A, the output signal ofmicroelectromechanical resonator 12 a includes a resonant frequency f₁which varies over operating temperature, and (ii) the output signal ofmicroelectromechanical resonator 12 b includes a resonant frequency f₂which also varies over operating temperature, an output signal having afrequency (f_(m)) that is substantially stable over temperature.

Notably, with reference to FIG. 12B, it may be advantageous toreconsider and/or evaluate the practical consideration of the design ofoscillator system 10 after designing/defining features of oscillatorsystem 10. For example, should the design present challenging processconstraints, frequency ranges, frequency tolerances, and a limitedoperating temperature range for one or more of the resonator structures,it may be advantageous to reconsider one or more of the materialproperties and/or parameters of the resonator structure(s). (See, 26 e).

The process flows of FIGS. 12A and 12B are merely exemplary in thecontext of microelectromechanical resonators 12 having the sametemperature dependence characteristics (for example, having the samesign of the first order derivative with respect to temperature). Wherethe temperature dependence characteristics of microelectromechanicalresonators 12 are opposite (for example, having the different signs ofthe first order derivative with respect to temperature), the design ofmicroelectromechanical resonators 12 assume the implementation of the“sum” component of frequency manipulation circuitry 14. All techniques,processes, and/or criteria, to determine appropriate features ofoscillator system 10 for a given frequency response, whether now knownor later developed, are intended to fall within the scope of the presentinventions.

Notably, further stability of the frequency (f_(m)) of the output signalof frequency manipulation circuitry 14 (relative to temperaturevariations) may be obtained upon consideration of second and higherorder terms. With respect to the second order terms, the adverse impactof the second order terms may be minimized, eliminated and/or reduced byproviding $\frac{f_{1{T{(0)}}}}{f_{2{T{(0)}}}}$equal to, or approximately equal to, $\frac{b_{2}}{b_{1}}.$Under these circumstances, the stability of the frequency (f_(mT(0))) ofthe output signal of frequency manipulation circuitry 14 (relative totemperature variations) may be enhanced thereby further reducing,limiting and/or minimizing the temperature dependence thereof.

Thus, providing a configuration whereby$\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}}$may enhance the stability of the frequency (f_(m)) of the output signalof frequency manipulation circuitry 14 (relative to temperaturevariations) thereby further reducing, limiting and/or minimizing thetemperature dependence thereof. Indeed, further stability may beobtained with consideration of third or larger order terms.

Notably, in one embodiment, the output signal of oscillator system 10 ineach instance includes desired, selected and/or predeterminedcharacteristics (for example, desired, selected and/or predeterminedfrequency) at a given, predetermined and/or particular frequency and/ortemperature. The output signal of oscillator system 10 in each instancemay also include desired, selected and/or predetermined characteristicsfor a frequency, over a set or range of frequencies and/or set or rangeof temperatures. For example, with reference to FIG. 5A, the frequencyversus temperature of the output signal of oscillator system 10 issubstantially stable (i.e., constant, substantially constant and/oressentially constant) and, as such, the frequency remains constant (orsubstantially constant) over a range of temperatures (for example, theoperating temperatures of oscillator system 10 and/or one or more ofresonators 12).

There are many inventions described and illustrated herein. Whilecertain embodiments, features, materials, configurations, attributes andadvantages of the inventions have been described and illustrated, itshould be understood that many other, as well as different and/orsimilar embodiments, features, materials, configurations, attributes,structures and advantages of the present inventions that are apparentfrom the description, illustration and claims (are possible by oneskilled in the art after consideration and/or review of thisdisclosure). As such, the embodiments, features, materials,configurations, attributes, structures and advantages of the inventionsdescribed and illustrated herein are not exhaustive and it should beunderstood that such other, similar, as well as different, embodiments,features, materials, configurations, attributes, structures andadvantages of the present inventions are within the scope of the presentinventions.

For example, in one embodiment, the frequency spectrum of the outputsignal of frequency manipulation circuitry 14 may be “shaped” in orderto provide a predetermined response that varies over operatingtemperature. In this regard, with reference to FIG. 13, thetemperature-dependent response of the output signal of frequencymanipulation circuitry 14 may be selected to provide a desired responseover a predetermined temperature range and/or at one or more particulartemperatures.

The frequency manipulation circuitry 14 providing “shaped” frequencyresponse over operating temperature generates a signal that is dependenton the operating temperature of one or more of resonators 12 a and 12 b.The control circuitry 22 may be employed to interpret, analyze and/orcorrelate the frequency of the output signal to an operatingtemperature. The control circuitry 22, as mentioned above, may employ alook-up table (based on empirical and/or theoretical data) and/or apredetermined or mathematical relationship to interpret, analyze and/orcorrelate the frequency of the output signal to an operatingtemperature. The control circuitry 22 may generate and/or providetemperature sensor data which is representative of the operatingtemperature to other circuitry.

In another embodiment, control circuitry 22 may adjust, correct and/orcontrol one or more of resonators 12 to, for example, provide a signalhaving a frequency within a given, predetermined and/or desired range.In this regard, in one embodiment, control circuitry 22 may instructand/or cause resonator drive and sense circuitry 24 to adjust, forexample, the bias drive for one or more of microelectromechanicalresonators 12. In this way, control circuitry 22 may “force” thecharacteristics of the output signal (for example, frequency) of one ormore of microelectromechanical resonators 12 to adjust the output signalof frequency manipulation circuitry 14 to provide a desired and/orpredetermined frequency (for example, where the frequency provides azero slope (here, f_(m)) or “turn-over” region or frequency aroundfrequency f_(m).

The control circuitry 22 may adjust and/or control frequencymanipulation circuitry 14 and/or resonators 12 in situ. Notably, alloperations and/or functions described above with respect to controlcircuitry 22 are applicable to this embodiment. For the sake of brevity,those discussions will not be repeated.

In certain embodiments, incorporating an “offset term” may alsofacilitate compensating and/or addressing any second or highertemperature dependent terms. For example, not entirely canceling thefirst-order frequency function of temperature may facilitate shaping ofthe residual second order response, reducing the maximum absolute changeover temperature of the output frequency function of temperature. Inthis case, the residual first-order term is referred to as an “offsetterm”. As mentioned above, although$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}$may enhance the stability of the frequency (f_(m)) of the output signalof frequency manipulation circuitry 14 (relative to temperaturevariations) by reducing, limiting, minimizing and/or eliminating theadverse affects of second or larger order terms, where thecharacteristics of the material and/or the architecture or design of oneor more microelectromechanical resonators 12 prohibit, limit and/orprevent the effects of the second or larger order terms (regardless ofreason), an “offset term” may be employed to adjust, address and/orcompensate for the temperature impact on the frequency of the output offrequency manipulation circuitry 14 due to second or higher temperaturedependent terms.

Notably, the frequency vs. temperature curve may be shaped byselectively canceling, partially-canceling, or adjusting thetemperature-dependent terms. For instance, the first and third-ordertemperature dependence may be “canceled”, but the second-orderdependence may not be canceled, or fully canceled, thereby providing afrequency turnover point for temperature-controlled oscillatorapplications. Moreover, a portion of the first-order temperaturedependence may be used to “shift” the position of the turnover point.

For temperature-stable oscillators, where microelectromechanicalresonators 12 a and 12 b of oscillator 10 do not have thecharacteristics to eliminate, minimize and/or reduce both first andsecond-order temperature dependence, oscillator 10 may include three ormore microelectromechanical resonators 12. With reference to FIGS. 14Aand 14B, in this embodiment, the output signals from three or moremicroelectromechanical resonators 12 may be applied to frequencymanipulation circuitry 14 and thereby “combined” (for example, added orsubtracted in appropriate combinations) to eliminate, minimize and/orreduce first and second-order (and/or higher order terms) temperaturedependence. In this regard, one or more additionalmicroelectromechanical resonators 12 c or 12 c-12 n, respectively, maybe employed, as represented in the equation immediately below, tocancel, minimize, reduce and/or eliminate at least one of the higherorder temperature-dependent terms in the equation:f _(m)(T)=±f ₁(T)±f ₂(T)±f ₃(T)± . . .

Notably, the sign in the equation immediately above may be “selected” toprovide for one or more predetermined temperature-dependence terms tocancel, offset and/or reduce, eliminate and/or minimize its impact onthe output frequency.

As an example, it may be advantageous to subtract the frequencies ofeach of microelectromechanical resonators 12 b and 12 c frommicroelectromechanical resonator 12 a (where oscillator 10 includesresonators 12 a-12 c) from 12 a. As such, f_(m)(T)=f₁(T)−f₂ (T)−f₃ (T).Under these circumstances,a ₁ f _(1T(0)) −a ₂ f _(2T(0)) −a ₃ f _(3T(0))=0b ₁ f _(1T(0)) −b ₂ f _(2T(0)) −b ₃ f _(3T(0))=0f _(1T(0)) −f _(2T(0)) −f _(3T(0)) =f _(mT(0))Thereafter, the equations may be solved for f_(1T(0)), f_(2T(0)), andf_(3T(0)). Notably, the solution to these equations may be, in part,dependent upon the materials selected for each resonator, and therelationship between the parameters a₁, a₂, a₃, b₁, b₂, b₃ in thesematerials.

Further, cancellation of first and higher-order temperature terms neednot be done sequentially. For example, microelectromechanical resonators12 a and 12 b may be used to cancel the second-order temperaturedependence, and not cancel the first-order temperature dependence. Thatis, the output signals microelectromechanical resonators 12 a and 12 bmay be applied to frequency manipulation circuitry 14 and thereby“combined” (for example, added or subtracted in appropriatecombinations) to eliminate, minimize and/or reduce second-order (and/orhigher order terms) temperature dependence and not the first-ordertemperature dependence term. Notably, canceling the second andhigher-order terms while not canceling the first-order may be used tosense the operating temperature of the microelectromechanicalresonators. In this case, a large change in the output frequency withrespect to temperature is desired, and a linear response is desired. Themethods employed above may be used to minimize, cancel, or reduce theeffect of the second-order terms, while substantially leaving thefirst-order terms of the frequency function of temperature.

As mentioned above, microelectromechanical resonators 12 may employ anytype of microelectromechanical resonator design, architecture and/orcontrol, whether now known or later developed. Indeed,microelectromechanical resonators 12 may be components or portions ofthe same physical structure (see, for example, FIG. 7C) and/ormicroelectromechanical resonators 12 may be the same component orportion of the same physical structure that resonate in multiple,different modes of operation, for example, in-plane and out-of-plane(see, for example, FIG. 7D). Further, microelectromechanical resonator12 may be fabricated and/or packaged using any fabrication and/orpackaging techniques, whether now known or later developed. As such, allsuch fabrication and/or packaging techniques are intended to fall withinthe scope of the present inventions.

The microelectromechanical resonators 12 may or may not include controlcircuitry that monitors, alters, controls and/or adjusts the operatingtemperature of microelectromechanical resonators 12 and/or frequency ofthe output signal of structure 12. All techniques for altering,controlling and/or adjusting the operation of microelectromechanicalresonator structure 12, whether now known or later developed, areintended to be within the present inventions.

Moreover, with reference to FIGS. 15A and 15B, as mentioned above, inone embodiment, the output signal of oscillator system 10 (having thesubstantially stable frequency over operating temperature) may beemployed as an output signal and/or may be applied to signal or clockalignment circuitry 28. Indeed, clock alignment circuitry 28, forexample, FLL(s), PLL(s), DLL(s) and/or digital/frequency synthesizer(s),may be cascaded in series so that a particular, precise and/orselectable frequency and phase are obtained. Notably, the operation andimplementation of FLL(s), PLL(s), DLL(s), and/or digital/frequencysynthesizer(s) (for example, DDS(s)) are well known to those skilled inthe art. Any FLL, PLL (whether fractional or integer), DLL (whetherfractional or integer) and/or digital/frequency synthesizers, as well asconfiguration thereof or alternatives therefor, whether now known orlater developed, is intended to fall within the scope of the presentinventions. Indeed, any clock or signal alignment circuitry 28, whethernow known or later developed, may be employed to generate an outputsignal having precise and stable characteristics (for example, frequencyand/or phase).

Moreover, the PLL, DLL, digital/frequency synthesizer and/or FLL mayalso compensate using multiplication and/or division to adjust, correct,compensate and/or control the characteristics (for example, thefrequency, phase and/or jitter) of the output signal ofmicroelectromechanical resonators 12 and/or the frequency manipulationcircuitry 14. The multiplication or division (and/or phase adjustments)by clock alignment circuitry 28 may be in fine or coarse increments. Forexample, clock alignment circuitry 28 may include an integer PLL, afractional PLL and/or a fine-fractional-N PLL to precisely select,control and/or set the output signal of microelectromechanicaloscillator system 10. In this regard, the output of frequencymanipulation circuitry 14 may be provided to the input of thefractional-N PLL and/or the fine-fractional-N PLL (hereinaftercollectively “fractional-N PLL”), which may be pre-set, pre-programmedand/or programmable (in memory 30) to provide an output signal having adesired, selected and/or predetermined frequency and/or phase.

Notably, in one embodiment, the parameters, references (for example,frequency and/or phase), values and/or coefficients employed by clockalignment circuitry 28 in order to generate and/or provide apredetermined, adjusted, corrected and/or controlled output having, forexample, a desired, selected and/or predetermined frequency and/or phase(i.e., the function of clock alignment circuitry 28), may be externallyprovided to clock alignment circuitry 28 either before or duringoperation of microelectromechanical oscillator system 10. In thisregard, a user or external circuitry/devices/systems may provideinformation representative of the parameters, references, values and/orcoefficients to set, change, enhance and/or optimize the performance ofclock alignment circuitry 28 and/or microelectromechanical oscillatorsystem 10.

As mentioned above, the output signal of microelectromechanicaloscillator system 10 may be single ended or double ended (i.e.,differential signaling). The “shape” of the output signal (for example,square, pulse, sinusoidal or clipped sinusoidal) may be predeterminedand/or programmable. In this regard, information which is representativeof the “shape” of the output signal may be stored or programmed inmemory (which is resident in frequency manipulation circuitry 14 and/orclock alignment circuitry 28 (if any) during fabrication, test,calibration and/or operation). In this way, frequency manipulationcircuitry 14 and/or clock alignment circuitry 28 may access residentmemory 30 (which may be integrated on the substrate with clock alignmentcircuitry 28) to obtain such information during start-up/power-up,initialization, re-initialization and/or during normal operation offrequency manipulation circuitry 14 and/or clock alignment circuitry 28.

The clock alignment circuitry 28 may be disposed on/in the samesubstrate or on/in different substrates as microelectromechanicalresonators 12 and/or frequency manipulation circuitry 14. (See, forexample FIGS. 16A-C). All permutations and combinations thereof areintended to fall within the scope of the present inventions. Moreover,the present inventions may employ any interconnect or interconnectiontechnique/architecture whether now known or later developed; all suchtechniques/architectures are intended to fall within the scope of thepresent inventions.

In one embodiment, one or more of microelectromechanical resonatorstructure 12 may be “replaced” by an electronic or electrical resonatorcircuit (for example, a capacitor/inductor circuit that, whenstimulated/activated, resonates at a given or predetermined frequency).In this regard, with reference to FIGS. 17A, 17D and 17E, in oneexemplary embodiment, electronic/electrical resonator circuit 32provides a signal having a frequency that depends on the operatingtemperature of the elements of electronic/electrical resonator circuits32, the design of resonator circuits 32, and the properties of thematerial comprising such elements. With reference to FIGS. 17B and 17C,in one exemplary embodiment, electronic/electrical resonator circuits 32a and 32 b each provide a signal having a frequency that depends on theoperating temperature of the elements of electronic/electrical resonatorcircuit 32 and the design and properties of the material comprising suchelements.

Similar to the embodiments described and illustrated above, oscillatorsystem 10 may be configured to provide and/or generate one or moreoutput signals having a predetermined frequency over temperature, forexample, (1) an output signal having a substantially stable frequencyover a predetermined range of operating temperatures and/or (2) anoutput signal having a frequency that is dependent on the operatingtemperature from which the operating temperature may be determined (forexample, an estimated operating temperature based on a empirical dataand/or a mathematical relationship).

With reference to FIGS. 17A-17M, oscillator system 10 may include one ormore electronic/electrical resonator circuits 32. Where oscillatorsystem 10 includes two electronic/electrical resonator circuits 32 a and32 b, each resonator system includes one or more material or designproperties that respond differently to temperature (relative to theother resonator circuit). The output of electronic/electrical resonatorcircuit 32, having a frequency which varies temperature, may be appliedto frequency manipulation circuitry 14 to generate an output signalhaving a predetermined frequency that is substantially stable overtemperature. The frequency manipulation circuitry 14 may, in addition toor in lieu thereof, generate an output signal having a predeterminedfrequency that changes over temperature in a predetermined manner.

Like the other embodiments described above in the context ofmicroelectromechanical resonators 12, in one embodiment of this aspectof the inventions, the output signal (of frequency manipulationcircuitry 14) having the substantially stable frequency over temperaturemay be employed as an output signal and/or may be applied to clockalignment circuitry 28. (See, for example, FIGS. 17L and 17M). In thisway, the clock signal may include a predetermined frequency that ishigher or lower in frequency than the frequency of the output signal ofthe oscillator system. Indeed, the clock alignment circuitry 28 mayprovide a plurality of output signals that are higher and/or lower infrequency than the frequency of the output signal of the oscillatorsystem.

Where the output signal of frequency manipulation circuitry 14 changesover temperature in a predetermined manner, that signal may be employedas a measure of the operating temperature of the system. In oneembodiment, the signal which is representative of the operatingtemperature of oscillator system 10 may be applied to control circuitry22 to interpret, analyze and/or correlate the frequency of the signalwhich is the dependent on the operating temperature. (See, for example,FIGS. 17D and 17G). Notably, all operations and/or functions describedabove with respect to control circuitry 22 are applicable to thisembodiment. Moreover, all permutations and combinations employingcontrol circuitry 22 and/or resonator drive and sense circuitry 24, inconjunction with one or more electronic/electrical resonator circuits32, are intended to fall within the scope of the present inventions.(See, for example, FIGS. 17F, 17G, 17H, 17J and 17K. For the sake ofbrevity, those discussions will not be repeated.

Notably, each of the aspects of the present inventions, and/orembodiments thereof, may be employed alone or in combination with one ormore of such aspects and/or embodiments. For the sake of brevity, thosepermutations and combinations will not be discussed separately herein.As such, the present inventions are not limited to any single aspect orembodiment thereof nor to any combinations and/or permutations of suchaspects and/or embodiments.

While the present inventions have been described in the context ofmicroelectromechanical systems including micromechanical resonators, thepresent inventions are not limited in this regard. Rather, theinventions described herein are applicable to gyroscopes, resonators,temperature sensors, accelerometers and/or other transducers as well asother electromechanical systems including, for example,nanoelectromechanical systems. Moreover, the oscillator system of thepresent inventions may be employed and/or embedded in any electricaldevice, for example, in which the oscillator output is used tocoordinate or synchronize operations and/or provide one or more clocksignals (for example, in a wired, wireless, or optical fiber networkcommunication system, in which transmit and receive circuits synchronizewith each other, or synchronization of multiple oscillators on ahigh-speed electronics chip designed to minimize clock signal skew, orsynchronizing components across a board or a communication bus) and/orin any electrical device in which temperature related information isemployed.

It should be further noted that the term “circuit” may mean, among otherthings, a single component (for example, electrical/electronic and/ormicroelectromechanical) or a multiplicity of components (whether inintegrated circuit form or otherwise), which are active and/or passive,and which are coupled together to provide or perform a desired function.The term “circuitry” may mean, among other things, a circuit (whetherintegrated or otherwise), a group of such circuits, one or moreprocessors, one or more state machines, one or more processorsimplementing software, or a combination of one or more circuits (whetherintegrated or otherwise), one or more state machines, one or moreprocessors, and/or one or more processors implementing software. Theterm “data” may mean, among other things, a current or voltage signal(s)whether in an analog or a digital form.

The term “frequency function of temperature” of a microelectromechanicalresonator may mean, among other things, the change in frequency of aresonator due to a change in Young's modulus over temperature of themicroelectromechanical resonator, the change in thermal coefficient ofexpansion of the microelectromechanical resonator over temperature, thechange in mass of the microelectromechanical resonator over temperature,and/or the change in stress/strain conditions of themicroelectromechanical resonator, the substrate and/or the housing.

1. An oscillatory system, comprising: a first microelectromechanical resonator to generate a first output signal having a frequency that varies with operating temperature, wherein the first microelectromechanical resonator includes a frequency function of temperature of the first microelectromechanical resonator; a second microelectromechanical resonator to generate a second output signal having a frequency that varies with operating temperature, wherein the second microelectromechanical resonator includes a frequency function of temperature of the second microelectromechanical resonator; and frequency manipulation circuitry, coupled to the first and second microelectromechanical resonators to generate a third signal having frequency that is substantially stable over a predetermined operating temperature using the first and second output signals.
 2. The oscillator system of claim 1 wherein the frequency manipulation circuitry is frequency subtraction circuitry.
 3. The oscillator system of claim 2 wherein the frequency subtraction circuitry is frequency mixer circuitry.
 4. The oscillator system of claim 3 wherein the frequency subtraction circuitry further includes filter circuitry, coupled to the frequency mixer circuitry, to receive an output of the frequency mixer circuitry and to filter a frequency sum component of the output of the frequency mixer circuitry.
 5. The oscillator system of claim 3 wherein the frequency mixer circuitry includes digital or analog circuitry.
 6. The oscillatory system of claim 1 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are disposed in or on the same substrate.
 7. The oscillator system of claim 6 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are fabricated from the same material.
 8. The oscillator system of claim 6 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are the same physical structure.
 9. The oscillator system of claim 6 wherein the first microelectromechanical resonator and the second micromechanical resonator include different crystalline orientations or directions in or on the same substrate.
 10. The oscillator system of claim 1 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are disposed in or on the different substrates.
 11. The oscillator system of claim 10 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are fabricated from different materials.
 12. The oscillator system of claim 1 wherein the first microelectromechanical resonator, the second microelectromechanical resonator and the frequency manipulation circuitry are disposed in or on the same substrate.
 13. An oscillator system, comprising: a first microelectromechanical resonator to generate a first output signal having a frequency that varies with operating temperature, wherein the first microelectromechanical resonator includes a frequency function of temperature of the first microelectromechanical resonator; a second microelectromechanical resonator to generate a second output signal having a frequency that varies with operating temperature, wherein the second microelectromechanical resonator includes a frequency function of temperature of the second microelectromechanical resonator; and frequency mixer circuitry, coupled to the first and second microelectromechanical resonators to generate a third signal having frequency that is substantially stable over an operating temperature using the first and second output signals.
 14. The oscillator system of claim 13 wherein the frequency mixer circuitry further includes filter circuitry, coupled to the frequency mixer circuitry, to receive an output of the frequency mixer circuitry and to filter a frequency sum component of the output of the frequency mixer circuitry.
 15. The oscillatory system of claim 13 wherein the frequency mixer circuitry includes digital or analog circuitry.
 16. The oscillatory system of claim 13 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are disposed in or on the same substrate.
 17. The oscillator system of claim 16 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are fabricated from the same material.
 18. The oscillator system of claim 16 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are the same physical structure.
 19. The oscillator system of claim 16 wherein the first microelectromechanical resonator and the second microelectromechanical resonator include different crystalline orientations or directions in or on the same substrate.
 20. The oscillator system of claim 13 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are disposed in or on the different substrates.
 21. The oscillator system of claim 20 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are fabricated from different materials.
 22. The oscillator system of claim 13 wherein the operating temperatures of the first and second microelectromechanical resonators substantially overlap with the predetermined operating temperature.
 23. An oscillator system, comprising: a first microelectromechanical resonator to generate a first output signal having a frequency that varies with operating temperature, wherein the first microelectromechanical resonator includes a frequency function of temperature of the first microelectromechanical resonator; a second microelectromechanical resonator to generate a second output signal having a frequency that varies with operating temperature, wherein the second microelectromechanical resonator includes a frequency function of temperature of the second microelectromechanical resonator; frequency mixer circuitry, coupled to the first and second microelectromechanical resonators to generate a third signal having frequency that is substantially stable over an operating temperature using the first and second output signals; and signal alignment circuitry, coupled to the frequency mixer circuitry, to generate an output signal having a frequency that is greater than or less than the frequency of the third signal.
 24. The oscillator system of claim 23 wherein the frequency mixer circuitry further includes filter circuitry, coupled to the frequency mixer circuitry, to receive an output of the frequency mixer circuitry an to filter a frequency difference component or frequency sum component of the output of the frequency mixer circuitry.
 25. The oscillator system of claim 24 wherein the signal alignment circuitry receives the output of the filter circuitry.
 26. The oscillator system of claim 24 wherein the frequency mixer circuitry includes digital or analog circuitry.
 27. The oscillator system of claim 24 wherein the signal alignment circuitry includes one or more phase locked loops, delay locked loops, digital/frequency synthesizer and/or frequency locked loops.
 28. The oscillator system of claim 27 wherein the one or more digital/frequency synthesizers include one or more direct digital synthesizers, frequency synthesizers, fractional synthesizers and/or numerically controlled oscillators.
 29. The oscillator system of claim 27 wherein the one or more phase locked loops, delay locked loops, digital/frequency synthesizer and/or frequency locked loops include fractional and/or fine-fractional type phase locked loops, delay locked loops, digital/frequency synthesizer and/or frequency locked loops.
 30. The oscillator system of claim 23 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are disposed in or on the same substrate.
 31. The oscillator system of claim 30 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are fabricated from the same material.
 32. The oscillator system of claim 30 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are the same physical structure.
 33. The oscillator system of claim 30 wherein the first microelectromechanical resonator and the second microelectromechanical resonator include different crystalline orientations or directions in or on the same substrate.
 34. The oscillator system of claim 23 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are disposed in or on the different substrates.
 35. The oscillator system of claim 34 wherein the first microelectromechanical resonator and the second microelectromechanical resonator are fabricated from different materials.
 36. The oscillator system of claim 23 wherein the operating temperature of the first microelectromechanical resonator and the operating temperature of the second microelectromechanical resonator substantially overlap with the operating temperature.
 37. The oscillator system of claim 23 wherein the first and second microelectromechanical resonators, the frequency miser circuitry, and the signal alignment circuitry are disposed in or on the same substrate. 